- Docente: Stanislav Smirnov
Our goal is to give an introduction to a beautiful area at the intersection of combinatorics and probability.
Dimer model considers coverings of all vertices of a graph by non-intersecting edges.
For a square grid 8x8, for example, this amounts to coverings of a chessboard by dominoes.
One can ask many questions:
- when can one tile a board by dominoes?
- how many coverings are there?
- how does a random covering look like?
- why for some boards random coverings have "frozen" regions.
We will discuss these questions and connections of dimers to other models, such as the Ising's ferromagnet